restrictions on β'xt and the asymptotic variance for the stochastic trends parameters,
oq1. How to specify deterministic components in the I(2) model is discussed at some
length. Model specification and tests are illustrated with an empirical analysis of long
and persistent swings in the foreign exchange market between Germany and USA. The
data analyzed consist of the nominal exchange rate, relative goods prices, the U.S.
inflation rate, and German and U.S. long-term and short-term interest rates over the
1975-1999 period during which the $/Dmk rate was floating.
It is clear from the past three decades of floating currencies that exchange rates have
a tendency to undergo persistent swings away from purchasing power parity (PPP) for
extended periods of time only to be followed by time periods in which exchange rates
move persistently towards this benchmark. International macro economists have long
puzzled over the long-swings behavior of floating exchange rates. They have uncov-
ered much evidence that, although departures from PPP are ultimately bounded, the
rate at which they damp out is much too slow to be consistent with the standard sticky-
price monetary model of Dornbusch (1976) or its New Open Economy Macroeconomics
formulations. Slow adjustment can be rationalized with the aid of an equilibrium model
(Stockman, 1980, among others), but the volatility of real exchange rates (that is, the
volatility of departures from PPP) is much too large to be consistent with these mod-
els.1 The inability of exchange rate theory to explain both the high volatility and high
persistence of real exchange rates is called the PPP puzzle.
As Dornbusch himself had recognized, his influential monetary model of the ex-
change rate is grossly inconsistent with the long-swings behavior of exchange rates.2
Frydman and Goldberg (2007) (hereafter FG) show, however, that once the Rational
Expectations Hypothesis (REH) is replaced with an Imperfect Knowledge Economics
(IKE) representation of forecasting behavior, the traditional monetary model is able
to generate exchange rate swings away from PPP.3 Such behavior can occur in the
model even if goods prices are assumed to be fully flexible and market participants are
assumed to form their forecasts solely on the basis of macroeconomic fundamentals. In
Frydman, Goldberg and Juselius (2007) (hereafter FGJ), the authors show that this
IKE model provides a resolution to the PPP puzzle: with exchange rate swings, goods
prices can adjust quickly to equilibrium levels while departures from PPP can damp
out very slowly. The empirical analysis provided in FGJ and the one in the present
paper are both based on estimating a cointegrated I(2) model of the exchange rate,
relative goods prices, and short- and long-run interest rates using the methodology
outlined here. To provide support for its resolution of the PPP puzzle, however, FGJ
focuses on only a subset of the results from the I(2) model. By contrast, in the present
1For reviews of the PPP literature, see Rogoff (1996), Taylor and Taylor (2004), Taylor and Sarno
(2003), and Mark (2003).
2For example, see Dornbusch and Frankel (1983).
3In contrast to the REH and behavioral models of aggregate outcomes, IKE only partially pre-
specifies how individual forecasting strategies might change over time. By only partially prespecifying
change, IKE models are able to recognize the importance of imperfect knowledge without presuming
that individuals are irrational. For an extensive comparsion of IKE and extant approaches to modeling
individual forecasting behvaior see part I and chapter 6 in Frydman and Goldberg (2007).